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Using the Power Rule · Physics Playground

Exercises Expressions, exponents and radicals

Example 3 from Algebra and Trigonometry, 1.2 Exponents and Scientific Notation

Using the Power Rule

Write each of the following products with a single base. Do not simplify further.

ⓐ ${(x^{2})}^{7}$
ⓑ ${({(2 t)}^{5})}^{3}$
ⓒ ${({(−3)}^{5})}^{11}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
Use the power rule to simplify each expression.
1. ⓐ ${(x^{2})}^{7} = x^{2 \cdot 7} = x^{14}$
2. ⓑ ${({(2 t)}^{5})}^{3} = {(2 t)}^{5 \cdot 3} = {(2 t)}^{15}$
3. ⓒ ${({(−3)}^{5})}^{11} = {(−3)}^{5 \cdot 11} = {(−3)}^{55}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write each of the following products with a single base. Do not simplify further.

ⓐ ${({(3 y)}^{8})}^{3}$
ⓑ ${(t^{5})}^{7}$

How did it go?

PreviousUsing the Quotient Rule Next Using the Zero Exponent Rule

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 1.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.

Solution

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