Write with a single exponent, 9^2(12^3)(2)

Question

asked Oct 6, 2023 115k views

2 Answers

Mark Wenzel · Answer 1 · 2023-10-07T01:17:49+0000

Answer:

6^7

Explanation:

9^2(12^3)(2)

$\mathsf{rewrite \ 9 \ as \ 3^2 } \implies 9^2=(3^2)^2$

Apply exponent rule
(a^b)^c=a^(bc) :

$\implies (3^2)^2=3^4$

$\mathsf{rewrite \ 12 \ as \ 2 \cdot 2 \cdot 3 } \implies 12^3=(2 \cdot 2 \cdot 3)^3$

Apply exponent rule
$(a\cdot b)^c=a^c \cdot b^c$

$\implies (2 \cdot 2 \cdot 3)^3=2^3 \cdot 2^3 \cdot 3^3$

$\mathsf{rewrite \ 2 \ as \ 2^1}$

Therefore,

$9^2(12^3)(2)=3^4 \cdot2^3\cdot2^3\cdot3^3\cdot2^1$

Gather like terms

$\implies 3^4\cdot3^3 \cdot2^3\cdot2^3\cdot2^1$

Apply exponent rule
$a^b \cdot a^c=a^(b+c)$ :

$\implies 3^(4+3)\cdot2^(3+3+1)$

$\implies 3^7 \cdot 2^7$

Apply exponent rule
$a^c \cdot b^c=(ab)^c$

$\implies (3 \cdot2)^7$

$\implies 6^7$