An exponent is a number that indicates how many times to multiply the base by itself. For example, in $$2^3$$ , 2 is the base and 3 is the exponent, meaning $$2 \times 2 \times 2$$ .

What is the value of $$(15^4)^x = 15^8$$ ?

To solve for x, use the power of a power property: $$15^{4x} = 15^8$$ , thus $$4x = 8$$ , leading to $$x = 2$$ .

How do you simplify $$ (5ab^2)^2 $$ ?

Use the power of a product property: $$5^2 \cdot a^2 \cdot (b^2)^2 = 25a^2b^4$$ .

What is the value of $$\frac{(-5)^{10}}{2^{35}}$$ ?

This expression simplifies to $$\frac{(-5)^{10}}{2^{35}}$$ , which cannot be simplified further without numerical values.

What is the value of $$4^3 \cdot 4^x = 4^{13}$$ ?

Using the product of powers property, we have $$4^{3+x} = 4^{13}$$ , thus $$3 + x = 13$$ , leading to $$x = 10$$ .

How do you simplify $$\frac{(-5)^3}{2^{-2}}$$ ?

Using the negative exponent rule, this simplifies to $$(-5)^3 \cdot 2^2 = -125 \cdot 4 = -500$$ .

What is $$a^0$$ equal to?

Any non-zero number raised to the power of zero is equal to 1, so $$a^0 = 1$$ .

What does $$(a^m)^n = a^{mn}$$ represent?

This is the power of a power property, which states that when raising a power to another power, you multiply the exponents.

What is the simplified form of $$\frac{(-5)^7}{2^{12}}$$ ?

This expression remains as $$\frac{(-5)^7}{2^{12}}$$ , which cannot be simplified further without numerical values.

What is the value of $$\frac{1}{16}$$ ?

This is a fraction representing one part of sixteen equal parts.

What does $$a^m \div a^n = a^{m-n}$$ mean?

This is the quotient of powers property, which states that when dividing two powers with the same base, you subtract the exponents.

How do you simplify $$\frac{(-5)^3}{2^2}$$ ?

This simplifies to $$\frac{-125}{4}$$ .

What is the value of $$\frac{1}{2^{-3}}$$ ?

Using the negative exponent rule, this simplifies to $$2^3 = 8$$ .

8th Grade Integer Exponents Flashcards

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1.

FLASHCARD QUESTION

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What is an exponent?

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2.

FLASHCARD QUESTION

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This is the product of powers property, which states that when multiplying two powers with the same base, you add the exponents.

3.

FLASHCARD QUESTION

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4.

FLASHCARD QUESTION

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5.

FLASHCARD QUESTION

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6.

FLASHCARD QUESTION

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This is the negative exponent rule, which states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent.

7.

FLASHCARD QUESTION

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