Exponents and Roots - Review

Answer explanation

To simplify \(3^4 \times 3^{-2}\), use the property of exponents: \(a^m \times a^n = a^{m+n}\). Thus, \(3^{4 + (-2)} = 3^{2}\). The correct answer is \(3^2\).

Tags

CCSS.8.EE.A.1

• 5

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Answer explanation

The value of \( \sqrt{49} \) is the number that, when multiplied by itself, equals 49. Since \( 7 \times 7 = 49 \), the correct answer is 7.

Tags

CCSS.8.EE.A.2

Express 5,000,000 in scientific notation.

Answer explanation

To express 5,000,000 in scientific notation, we write it as 5.0 multiplied by 10 raised to the power of 6, since there are 6 places to the right of the decimal point. Thus, the correct answer is 5 \times 10^6.

Tags

CCSS.8.EE.A.3

Answer explanation

To calculate (2 × 10^3) × (3 × 10^4), multiply the coefficients: 2 × 3 = 6, and add the exponents: 3 + 4 = 7. Thus, the result is 6 × 10^7, which matches the correct answer choice.

Tags

CCSS.8.EE.A.4

Answer explanation

To simplify (x^3)^4, use the power of a power rule: multiply the exponents. Thus, 3 * 4 = 12, giving us x^{12}. Therefore, the correct answer is x^{12}.

Tags

CCSS.8.EE.A.1

• 6

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Answer explanation

To solve for x in the equation x^2 = 64, take the square root of both sides. This gives x = ±8. Since we are looking for the positive solution, the correct answer is 8.

Tags

CCSS.8.EE.A.2

Express 0.00045 in scientific notation.

Answer explanation

To express 0.00045 in scientific notation, move the decimal point 5 places to the right, giving 4.5. This results in 4.5 x 10^{-5}, as the exponent is negative due to the original number being less than 1.

Tags

CCSS.8.EE.A.3

Tags

CCSS.8.EE.A.4

Answer explanation

To simplify \(5^{-2} \times 5^3\), use the property of exponents: \(a^m \times a^n = a^{m+n}\). Thus, \(-2 + 3 = 1\), giving \(5^1\) as the simplified expression. The correct answer is \(5^1\).

Tags

CCSS.8.EE.A.1

What is the cube root of 27?

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Answer explanation

The cube root of a number is a value that, when multiplied by itself three times, gives the original number. For 27, 3 x 3 x 3 = 27, so the cube root of 27 is 3.

Tags

CCSS.8.EE.A.2