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Exponents and Powers MATHS - Exponents and Powers

ICSE - STD 8 - MATHS (ICSE - English Medium). 102 questions in this chapter.

Question types

Exponents and Powers question types

102 questions across 8 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

102
Questions
8
Question groups
5
Question types
Sample Questions

Exponents and Powers questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 13[4 marks sum]4 Marks
Find the value of x when :
$\left[\left\{\left(\frac{2}{5}\right)^2\right\}^4\right]^{x+2}=\left[\left\{\left(\frac{2}{5}\right)^{-2}\right\}^{(x-1)}\right]^{-3}$
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Q 14[4 marks sum]4 Marks
Find the value of x when :
$\left(\frac{-3}{11}\right)^{x+5} \div\left(\frac{-3}{11}\right)^{-2 x+3}=\left(\frac{-3}{11}\right)^{2 x-5} \times\left[\left(\frac{-3}{11}\right)^{-2}\right]^{(x+4)}$
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Q 15[5 marks sum]5 Marks
Show that :
$\left(\frac{x^a}{x^b}\right)^{a^2+a b+b^2} \times\left(\frac{x^b}{x^c}\right)^{b^2+b c+c^2} \times\left(\frac{x^c}{x^a}\right)^{c^2+c a+a^2}=1$.
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Q 16[5 marks sum]5 Marks
Show that :
$\left(\frac{x^{a^2}}{x^{b^2}}\right)^{\frac{1}{a+b}} \times\left(\frac{x^{b^2}}{x^{c^2}}\right)^{\frac{1}{b+c}} \times\left(\frac{x^{c^2}}{x^{a^2}}\right)^{\frac{1}{c+a}}=1$.
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Q 17[5 marks sum]5 Marks
Show that :
$\left(\frac{x^{a+b}}{x^c}\right)^{a-b} \times\left(\frac{x^{b+c}}{x^a}\right)^{b-c} \times\left(\frac{x^{c+a}}{x^b}\right)^{c-a}=1$.
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Q 18[5 marks sum]5 Marks
Show that :
$\left(\frac{x^a}{x^{-b}}\right)^{a-b} \times\left(\frac{x^b}{x^{-c}}\right)^{b-c} \times\left(\frac{x^c}{x^{-a}}\right)^{c-a}=1$.
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Q 30MCQ1 Mark
Which of the following is the same as $\left(\frac{-5}{7}\right)^{-7}$ ?
  • A
    $\left(\frac{5}{7}\right)^{-7}$
  • B
    $-\left(\frac{5}{7}\right)^{-7}$
  • C
    $\left(\frac{7}{5}\right)^{7}$
  • ✓
    $\left(\frac{-7}{5}\right)^7$

Answer: D.

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Q 31MCQ1 Mark
$(64)^{\frac{-1}{2}}-(-32)^{\frac{-4}{5}}=?$
  • A
    $\frac{1}{8}$
  • B
    $\frac{3}{8}$
  • ✓
    $\frac{1}{16}$
  • D
    $\frac{3}{16}$

Answer: C.

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Q 32MCQ1 Mark
The value of $\left(8^{-1}-9^{-1}\right)^{-1} \div\left(4^{-1}-9^{-1}\right)^{-1}$ is
  • A
    5
  • ✓
    10
  • C
    14
  • D
    25

Answer: B.

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Q 33MCQ1 Mark
The value of $\left[2-3(2-3)^{-1}\right]^{-1}$ is
  • A
    5
  • B
    -5
  • ✓
    $\frac{1}{5}$
  • D
    $\frac{-1}{5}$

Answer: C.

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Q 34MCQ1 Mark
The value of $\left(\frac{32}{243}\right)^{-\frac{4}{5}}$ is
  • A
    $\frac{4}{9}$
  • B
    $\frac{9}{4}$
  • C
    $\frac{16}{81}$
  • ✓
    $\frac{81}{16}$

Answer: D.

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