Question
Simplify and express the result in power notation with positive exponent: $\left(3^{-7} \div 3^{-10}\right) \times 3^{-5}$
✓
Answer
$\left(3^{-7} \div 3^{-10}\right) \times 3^{-5}$
$ = \left( {\frac{{{3^{ - 7}}}}{{{3^{ - 10}}}}} \right) \times \frac{1}{{{3^5}}}$
$ = {3^{( - 7) - ( - 10)}} \times {3^{\frac{1}{5}}}$
$ = {3^{ - 7 + 10}} \times {3^{\frac{1}{5}}}$
$ = \frac{{{3^3}}}{{{3^5}}}$
$ = \frac{1}{{{3^{5 - 3}}}}$
$ = \frac{1}{{{{(3)}^2}}}$
$ = \left( {\frac{{{3^{ - 7}}}}{{{3^{ - 10}}}}} \right) \times \frac{1}{{{3^5}}}$
$ = {3^{( - 7) - ( - 10)}} \times {3^{\frac{1}{5}}}$
$ = {3^{ - 7 + 10}} \times {3^{\frac{1}{5}}}$
$ = \frac{{{3^3}}}{{{3^5}}}$
$ = \frac{1}{{{3^{5 - 3}}}}$
$ = \frac{1}{{{{(3)}^2}}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Expand the following, using suitable identities.$\Big(\frac{4\text{x}}{5}+\frac{\text{y}}{4}\Big)\Big(\frac{4\text{x}}{5}+\frac{3\text{y}}{4}\Big)$
→Evaluate:
$(218)^2- (217)^2$
→$(218)^2- (217)^2$
After the surface area of a cube is painted, the cube is cut into 64 smaller cubes of same dimensions (see the figure). How many have
(i) no face painted? $\qquad$ (ii) 1 face painted? $\qquad$
(iii) 2 faces painted? $\qquad$ (iv) 3 faces painted?
→(i) no face painted? $\qquad$ (ii) 1 face painted? $\qquad$
(iii) 2 faces painted? $\qquad$ (iv) 3 faces painted?
Write the following numbers in usual form:
$2.06 × 10^{-5}$
→$2.06 × 10^{-5}$
Evaluate:
$ 69 × 71$
→$ 69 × 71$
What numbers do these numerals stand for?
Solve: $8x + 3 = 27 + 2x$
→The area of a rectangle is $x^2+ 7x + 12$. If its breadth is $(x + 3)$, then find its length.
→If $\frac{6^n}{6^{-2}}=6^3$, then find the value of $n$
→Hardy-Ramanujan number 1729 is the smallest Hardy-Ramanujan number. There are infinitely many such numbers. Few are 4104 (2, 16; 9, 15), 13832 (18, 20 ; 2, 24). Check it with the numbers given in the brackets.