Question

$4^{3/4} * 2^{x} =16^{2/5}$

Answer 1

Answer:

$\sf x=\frac{1}{10}$

Step-by-step explanation:

Rewrite expression with bases of 4.

$\sf{4^{\frac{3}{4} }} \times \sf({4^\frac{1}{2} )^x =(4^2)^{\frac{2}{5} }$

Apply law of exponents, when bases are same for exponents in multiplication, add the exponents. When a base with an exponent has a whole exponent, then multiply the two exponents.

$\sf{4^{\frac{3}{4} }} \times \sf{4^{\frac{1}{2} x}=4^{\frac{4}{5} }$

$\sf{4^{\frac{3}{4} +\frac{1}{2} x}=4^{\frac{4}{5} }$

Cancel same bases.

$\sf \frac{3}{4} +\frac{1}{2} x=\frac{4}{5}$

Subtract 3/4 from both sides.

$\sf \frac{1}{2} x=\frac{1}{20}$

Multiply both sides by 2.

$\sf x=\frac{1}{10}$

Answer 2

Step-by-step explanation:

2^{2*3/4} × 2^{x}=2^{4×2/5}

2^{3/2} × 2^{x}= 2^{8/5}

2^{3/2+x}=2^{8/5}

equate powers

{3+2x}/2= 2^2

5{3+2x}= 2{8}

15+10x=16

collect like terms

10x=16-15

10x=1

divide both sides by 10

x=1/10

x=0.1