What is the product of $$d^2$$ and $$d^5$$ ?

$$d^{2+5} = d^7$$ , so the answer is $$2d^7$$ .

How do you simplify $$\text{(ab}^3\text{)}^2$$ ?

Use the power of a product rule: $$(ab^3)^2 = a^2b^{3 \times 2} = a^2b^6$$ .

What is the result of $$2nm^3 \times 3m^{-2}n^4$$ ?

Combine coefficients and add exponents: $$2 \times 3 = 6$$ , $$m^{3-2} = m^1$$ , $$n^{1+4} = n^5$$ , so the answer is $$6mn^5$$ .

How do you simplify $$-2n^{-2} \times 2m^{-2}n^2$$ ?

Combine coefficients and add exponents: $$-2 \times 2 = -4$$ , $$n^{-2+2} = n^0 = 1$$ , so the answer is $$-\frac{4}{m^2}$$ .

What is $$\text{(-4yx}^{-4})^{-2}$$ simplified?

Apply the power of a power rule: $$(-4)^{-2} = \frac{1}{16}$$ , $$x^{-4 \times -2} = x^8$$ , so the answer is $$\frac{x^8}{16y^2}$$ .

Explain how to simplify $$\frac{a^5}{a^2}$$ .

Subtract the exponents: $$a^{5-2} = a^3$$ .

What does $$a^{-n}$$ represent?

It represents the reciprocal: $$a^{-n} = \frac{1}{a^n}$$ .

How do you multiply exponents with the same base?

Add the exponents: $$a^m \times a^n = a^{m+n}$$ .

What is the result of $$x^3 \times x^4$$ ?

Add the exponents: $$x^{3+4} = x^7$$ .

Define the zero exponent rule.

Any non-zero number raised to the power of zero equals one: $$a^0 = 1$$ .

What is $$\frac{1}{x^{-3}}$$ simplified?

Use the negative exponent rule: $$\frac{1}{x^{-3}} = x^3$$ .

Explain how to simplify $$\frac{b^4}{b^2}$$ .

Subtract the exponents: $$b^{4-2} = b^2$$ .

What is the result of $$2^3 \times 2^2$$ ?

Add the exponents: $$2^{3+2} = 2^5 = 32$$ .

Simplifying Exponents Flashcards

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Define the power of a product rule.

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What is the power of a power rule?

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