Question

tell whether each equation is true or false.
equation | true or false?
$(5^6)^4 = 5^{10}$ | false
$3^5 \cdot 3^6 = 3^{11}$ | true
$\frac{6^{12}}{6^5} = 6^7$ | true
$(3 \cdot 2)^6 = 3 \cdot 2^6$ |?
| true
| false

Explanation:

Step1: Apply power of product rule

For $(a \cdot b)^n$, the rule is $(a \cdot b)^n = a^n \cdot b^n$. So:
$(3 \cdot 2)^6 = 3^6 \cdot 2^6$

Step2: Compare both sides

The right-hand side of the given equation is $3 \cdot 2^6$, while we found the left-hand side equals $3^6 \cdot 2^6$. Since $3^6
eq 3$, the two sides are not equal.

Answer:

False