Exponents - Properties

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What is an exponent?

Back

An exponent is a mathematical notation indicating the number of times a number (the base) is multiplied by itself.

Tags

CCSS.6.EE.A.1

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What is the product of powers property?

Back

The product of powers property states that when multiplying two expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).

Tags

CCSS.8.EE.A.1

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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: (a^m)^n = a^(m*n).

Tags

CCSS.8.EE.A.1

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 distribute the exponent to each factor: (ab)^n = a^n * b^n.

Tags

CCSS.8.EE.A.1

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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: a^0 = 1 (where a ≠ 0).

Tags

CCSS.8.EE.A.1

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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: a^(-n) = 1/(a^n) (where a ≠ 0).

Tags

CCSS.8.EE.A.1

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How do you simplify (3x^3)(4x^-2)?

Back

To simplify (3x^3)(4x^-2), multiply the coefficients (3*4) and add the exponents of x (3 + (-2)): 12x^(3-2) = 12x.

Tags

CCSS.HSA.APR.A.1

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What is the simplified form of (2a^2b^4z)(6a^3b^2z^5)?

Back

To simplify (2a^2b^4z)(6a^3b^2z^5), multiply the coefficients (2*6) and add the exponents for each variable: 12a^(2+3)b^(4+2)z^(1+5) = 12a^5b^6z^6.

Tags

CCSS.HSA.APR.A.1

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How do you simplify x * x^7 * x^3?

Back

To simplify x * x^7 * x^3, add the exponents: 1 + 7 + 3 = 11. The simplified form is x^11.

Tags

CCSS.HSA.APR.A.1

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What is the simplified form of (2x^4y^7)^3?

Back

To simplify (2x^4y^7)^3, apply the power of a product property: (2^3)(x^(4*3))(y^(7*3)) = 8x^12y^21.

Tags

CCSS.HSA.APR.A.1