Exponents and Powers - Gujarat Board (GSEB) STD 8 MATHS Questions

A particular star is at a distance of about $8.1 × 10^{13}$ km from the Earth. Assuring that light travels at $3 × 10^8$m per second, find how long does light takes from that star to reach the Earth.

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Q 113 Marks Question3 Marks

In a repeater machine with $0$ as an exponent, the base machine is applied $0$ times.
$a.$ What do these machines do to a piece of chalk?

$b.$ What do you think the value of $60$ is? You have seen that a hookup of repeater machines with the same base can be replaced by a single repeater machine. Similarly, when you multiply exponential expressions with the same base, you can replace them with a single expression.

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Q 123 Marks Question3 Marks

Simplify: $\big(\frac{4}{13}\big)^4\times\big(\frac{13}{7}\big)^2\times\big(\frac{7}{4}\big)^3$

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Q 133 Marks Question3 Marks

$\frac{16\times10^2\times64}{2^4\times4^2}$

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Q 143 Marks Question3 Marks

Simplify: $\frac{(3^{-2})^{2}\times(5^2)^{-3}\times(\text{t}^{-3})^2}{(3^{-2})^{5}\times(5^3)^{-2}\times(\text{t}^{-4})^3}$

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Q 153 Marks Question3 Marks

Find the value of x, so that:
$\left(2^{-1}+4^{-1}+6^{-1}+8^{-1}\right)^x=1$

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Q 165 Marks Questions5 Marks

Astronomy The table shows the mass of the planets, the sun and the moon in our solar system.

Celestial Body	Mass $(kg)$	Mass $(kg)$ Standard Notation
Sun	$1,990,000,000,000,000,000,000,000,000,000$	$1.99 \times 10^{30}$
Mercury	$330,000,000,000,000,000,000,000$
Venus	$4,870,000,000,000,000,000,000,000$
Earth	$5,970,000,000,000,000,000,000,000$
Mars	$642,000,000,000,000,000,000,000,000,000$
Jupiter	$1,900,000,000,000,000,000,000,000,000$
Saturn	$568,000,000,000,000,000,000,000,000$
Uranus	$86,800,000,000,000,000,000,000,000$
Neptune	$102,000,000,000,000,000,000,000,000$
Pluto	$12,700,000,000,000,000,000,000$
Moon	$73,500,000,000,000,000,000,000$

$a.$ Write the mass of each planet and the Moon in scientific notation.
$b.$ Order the planets and the moon by mass, from least to greatest.
$c.$ Which planet has about the same mass as earth?

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Q 175 Marks Questions5 Marks

Investigating Solar System: The table shows the average distance from each planet in our solar system to the sun.

Planet	Distance from sun $(km)$	Distance from sun $(km)$ Standard Notation
Earth	$149,600,000$	$1.496 \times 10^8$
Jupiter	$778,300,000$
Mars	$227,900,000$
Mercury	$57,900,000$
Neptune	$4,497,000,000$
Pluto	$5,900,000,000$
Saturn	$1,427,000,000$
Uranus	$2,870,000,000$
Venus	$108,200,000$

$a.$ Complete the table by expressing the distance from each planet to the Sun in scientific notation.

$b.$ Order the planets from closest to the sun to farthest from the sun.

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Q 185 Marks Questions5 Marks

Predicting the ones digit, copy and complete this table and answer the questions that follow.

$x$	$1^x$	$2^x$	$3^x$	$4^x$	$5^x$	$6^x$	$7^x$	$8^x$	$9^x$	$10^x$
$1$	$1$	$2$
$2$	$1$	$4$
$3$	$1$	$8$
$4$	$1$	$16$
$5$	$1$	$32$
$6$	$1$	$64$
$7$	$1$	$128$
$8$	$1$	$256$
Ones Digit of the Powers	$1$	$2, 4, 8, 6$

$a.$ Describe patterns you see in the ones digits of the powers.
$b.$ Predict the ones digit in the following:
$i. 4^{12}$
$ii. 9^{20}$
$iii. 3^{17}$
$iv. 5^{100}$
$v. 10^{500}$
$c.$ Predict the ones digit in the following:
$i. 31^{10}$
$ii. 12^{10}$
$iii.17^{21}$
$iv. 29^{10}$

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Q 195 Marks Questions5 Marks

An insect is on the $0$ point of a number line, hopping towards $1$. She covers half the distance from her current location to $1$ with each hop. So, she will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops, and so on.

$a.$ Make a table showing the insect’s location for the first $10$ hops.
$b.$ Where will the insect be after $n$ hops?
$c.$ Will the insect ever get to $1$? Explain.

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Q 205 Marks Questions5 Marks

This table shows the mass of one atom for five chemical elements. Use it to answer the question given.

Elements	Mass of atom $(kg)$
Titanium	$7.95 \times 10^{-26}$
Lead	$3.44 \times 10^{-25}$
Silver	$1.79 \times 10^{-25}$
Lithium	$1.15 \times 10^{-26}$
Hydrogen	$1.674 \times 10^{-27}$

$a.$ Which is the heaviest element?
$b.$ Which element is lighter, Silver or Titanium?
$c.$ List all five elements in order from lightest to heaviest.

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Q 211 Marks Question1 Mark

The value of $\Big(\frac{1}{2^3}\Big)^3$ is equal to _________.

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Q 221 Marks Question1 Mark

The value of $3 \times 10^{-7}$ is equal to ________.

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Q 231 Marks Question1 Mark

The usual form for $2 × 10^{-2}$ is not equal to $0.02.$

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Q 241 Marks Question1 Mark

To add the numbers given in standard form, we first convert them into numbers with ________ exponents.