Question

Simplify the following expression.

(7^5)^3 × 7^7
A. 7^8
B. 7^15
C. 7^56
D. 7^22

Answer 1

\(\bf (7^5)^3 \times 7^7\implies 7^{{\color{red}{ 5\cdot 3}}}\times 7^{\color{blue}{ 7}}\implies 7^{{\color{red}{ 5\cdot 3}}+{\color{blue}{ 7}}}\)

Answer 2

@jdoe0001 i don't understand??

Answer 3

First simplify (7^5)^3

Answer 4

We use the rule

(a^b)^c = a^(b*c) ... in other words, multiply the exponents

Answer 5

so

(7^5)^3 = 7^(5*3) = 7^(15)

Answer 6

That turns

(7^5)^3 × 7^7

into

7^(15) × 7^7

Answer 7

Now use the rule

a^b * a^c = a^(b+c) ... in other words, add the exponents

Answer 8

so it's 7^22?

Answer 9

7^(15) × 7^7 = 7^(15 + 7) = 7^(22)

So that means

(7^5)^3 × 7^7 = 7^(22)

Answer 10

@jim_thompson5910 yay thank you so much for explaining it out for me it makes much more sense now

Answer 11

you're welcome

Answer 12

its D

Answer 13

@samantha6233 i know thanks