Mathematics: Simplify the following exponential expression. show your work step by step and list the properties of exponents used to solve this problem next to your work. 3x^{0}(2x^{3}t^{2})^{4} (4x^{7}y^{4})^{2}

the answer is b I think not for sure...

Simplify the following exponential expression. show

Deascry

11.03.2022

Given problem is

$\frac{3x^0(2x^3t^2)^4}{(4x^7y^4)^2}$

distribute outer exponents using formula: $(a^mb^n)^c=a^{mc}b^{nc}$ , we get:

$=\frac{3x^0(2^4x^{3\cdot4}t^{2\cdot4})}{4^2x^{7\cdot2}y^{4\cdot2}}$

Simplify exponents:

$=\frac{3x^0(2^4x^{12}t^8)}{4^2x^{14}y^8}$

plug x^0=1

$=\frac{3\cdot1(2^4x^{12}t^8)}{4^2x^{14}y^8}$

simplify exponents

$=\frac{3(16x^{12}t^8)}{16x^{14}y^8}$

simplify (closure property)

$=\frac{48x^{12}t^8}{16x^{14}y^8}$

simplify exponent part using formula : $\frac{a^m}{a^n}=a^{\left(m-n\right)}$ we get:

$=\frac{3x^{\left(12-14\right)}t^8}{y^8}$

Simplify exponents:

$=\frac{3x^{\left(-2\right)}t^8}{y^8}$

send term to denominator to avoid negative exponent

$=\frac{3t^8}{x^2y^8}$

Hence final answer is $\frac{3t^8}{x^2y^8}$ .

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