Question

Simplify

Answer 1

Answer:

x⁸y³

Step-by-step explanation:

x⁵ ÷ y² × x³ × y⁵

It will be easier to solve this problem if you first rearrange the expression to associate like terms.

(x⁵ × x³) × (y⁵ ÷ y²)

Now, you can use the rules of exponents: When multiplying, you add exponents; when dividing, you subtract exponents.

x⁵ × x³ = x⁵⁺³ = x⁸  

y⁵ ÷ y² = y⁵⁻² = y³

Thus,

(x⁵ × x³) × (y⁵ ÷ y²) = x⁸y³

Answer 2

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ x^5\div y^2\times x^3\times y^5\implies \cfrac{x^5}{y^2}\cdot x^3\cdot y^5\implies x^5\cdot y^{-2}\cdot x^3\cdot y^5 \\\\\\ x^{5+3}y^{-2+5}\implies x^8y^3$