Exponents

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What is an exponent?

Back

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 is multiplied by itself 3 times (2 × 2 × 2 = 8).

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two powers with the same base, you add the exponents. For example, x^a * x^b = x^(a+b).

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What is the power of a power property?

Back

The power of a power property states that when raising a power to another power, you multiply the exponents. For example, (x^a)^b = x^(a*b).

Front

What is the power of a product property?

Back

The power of a product property states that when raising a product to a power, you can distribute the exponent to each factor. For example, (xy)^a = x^a * y^a.

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What is the zero exponent rule?

Back

The zero exponent rule states that any non-zero base raised to the power of zero equals one. For example, x^0 = 1 (where x ≠ 0).

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What is the negative exponent rule?

Back

The negative exponent rule states that a negative exponent indicates the reciprocal of the base raised to the opposite positive exponent. For example, x^(-a) = 1/(x^a).

Front

Expand (yz^4)(-y^7z^2)

Back

The expansion results in -y^8z^6.

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Simplify (y^3)(y)

Back

The simplification results in y^4.

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Simplify x^3 ⋅ x^2

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The simplification results in x^5.

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Expand (x^3)(x^3)

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The expansion results in x^6.