Question

PLEASE HELP WILL MARK BRAINLIEST!! rewriting exponential equations using the same base?

Answer 1

Answer:

$\large1) \sf {2}^{8x} = {2}^{5 x+ 15}$

$\large \: 2)\sf {2}^{ - 4x} = {2}^{2x + 2}$

Step-by-step explanation:

to understand this

you need to know about:

• law of exponent
• PEMDAS

let's solve:

1. $\sf rewrite \: 16 \: as \: {2}^{4} : \\ \sf {2}^{4(2x)} = {32}^{x + 3}$
2. $\sf rewrite \: 32 \: as \: {2}^{5} : \\ {2}^{4(2x)} = {2}^{5(x + 3)}$
3. $\sf distribute : \\ \sf {2}^{8x} = {2}^{5 x+ 15}$

let's figure out the second one:

1. $\sf rewrite \: \frac{1}{16} \: as \: {2}^{ - 4} : \\ \sf {2}^{ - 4(x)} = {4}^{x + 1}$
2. $\sf rewrite \: 4 \: as \: {2}^{2} : \\ \sf {2}^{ - 4(x)} = {2}^{2(x + 1)}$
3. $\sf distribute : \\ {2}^{ - 4x} = {2}^{2x + 2}$