Exponent Laws Quiz for Grade 9

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Tags

CCSS.6.EE.A.1

Answer explanation

To simplify the expression \(x^3 \cdot x^4\), use the property of exponents that states \(a^m \cdot a^n = a^{m+n}\). Thus, \(x^3 \cdot x^4 = x^{3+4} = x^7\). The correct answer is \(x^7\).

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify \( \frac{y^5}{y^2} \), subtract the exponents: \( 5 - 2 = 3 \). Thus, the expression simplifies to \( y^3 \), which is the correct answer.

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify (a^2)^3, use the power of a power rule: multiply the exponents. Thus, (a^2)^3 = a^(2*3) = a^6. Therefore, the correct answer is a^6.

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify the expression \(b^{-4} \cdot b^2\), use the property of exponents: \(b^m \cdot b^n = b^{m+n}\). Here, \(-4 + 2 = -2\), so the result is \(b^{-2}\), which is the correct answer.

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify \left(\frac{1}{x^3}\right)^2, apply the power of a quotient rule: \frac{1^2}{(x^3)^2} = \frac{1}{x^{3 \cdot 2}} = \frac{1}{x^6}. Thus, the correct answer is \frac{1}{x^6}.

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify the expression, use the property of exponents: \(m^{a} \cdot m^{b} = m^{a+b}\). Here, \(\frac{1}{2} + \frac{3}{2} = 2\). Thus, \(m^{\frac{1}{2}} \cdot m^{\frac{3}{2}} = m^2\), which is the correct answer.

Tags

CCSS.HSN.RN.A.2

Answer explanation

To simplify \( \frac{z^7}{z^{-3}} \), use the property of exponents: \( a^m / a^n = a^{m-n} \). Thus, \( z^{7 - (-3)} = z^{7 + 3} = z^{10} \). The correct answer is \( z^{10} \).

Tags

CCSS.8.EE.A.1

Answer explanation

To simplify (2x^3y^2)^2, apply the power of a product rule: (ab)^n = a^n b^n. Thus, (2^2)(x^{3*2})(y^{2*2}) = 4x^6y^4. The correct answer is 4x^6y^4.

Tags

CCSS.HSA.APR.A.1

Answer explanation

To simplify \( \frac{(3a^2b)^3}{9a^3b^2} \), first calculate the numerator: \( (3a^2b)^3 = 27a^6b^3 \). Then, divide by the denominator: \( \frac{27a^6b^3}{9a^3b^2} = 3a^{6-3}b^{3-2} = 3a^3b \). Thus, the simplified expression is \( a^3b \).

Tags

TEKS.MATH.A.11B