Question

1. is △abc congruent to △def? explain.

for problems 15 and 16, use the properties and definitions of exponents to write the expression as a single power.

1. ( 8^{2} cdot 2^{5} )
2. ( \frac{3^{5}}{9} )

Explanation:

for Problem 15:

Step1: Rewrite 8 as 2³

$8^2 = (2^3)^2 = 2^{3×2} = 2^6$

Step2: Multiply with 2⁵

$2^6 \cdot 2^5 = 2^{6+5} = 2^{11}$

for Problem 16:

Step1: Rewrite 9 as 3²

$\frac{3^5}{9} = \frac{3^5}{3^2}$

Step2: Subtract exponents

$3^{5-2} = 3^3$

Answer:

Problem 15: $2^{11}$
Problem 16: $3^3$