Here are five problems that involve the properties of exponents:

1. Product of Powers Property

Simplify:
$(3x^4)(5x^7)$

2. Quotient of Powers Property

Simplify:
$\frac{y^9}{y^5}$

3. Power of a Power Property

Simplify:
$(2a^3)^4$

4. Negative Exponent Property

Simplify:
$\frac{5^{-3} x^2}{x^{-4}}$

5. Zero Exponent Property

Evaluate:
$(10^5 + 2^3)^0$

Would you like me to solve them step by step?

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Related Problems:

1. Simplify: $(x^3 y^2)^5$
2. Evaluate: $\frac{4^{-2} \cdot 4^5}{4^3}$
3. Expand: $(ab^2)^4$
4. Express without negative exponents: $\frac{a^{-3} b^2}{b^{-5} a^4}$
5. If $2^x = 16$, find $x$.

Tip:

When simplifying expressions with exponents, always check whether you need to multiply, divide, or distribute the exponents before applying properties.