Questions: Write the expression without using a calculator. (a) 3^4 (b) -3^4 (c) 3^-4 (d) (2/3)^-2 (e) 16-3/4 Write your answer without negative exponents. (a) 50-sqrt(32) (b) (a^3 b^3)(4 a b^2)^2 (c) (3 x^(3/2) y^3)/(2^-2)

Write the expression without using a calculator. (a) 3^4 (b) -3^4 (c) 3^-4 (d) (2/3)^-2 (e) 16-3/4 Write your answer without negative exponents. (a) 50-sqrt(32) (b) (a^3 b^3)(4 a b^2)^2 (c) (3 x^(3/2) y^3)/(2^-2)
Transcript text: Write the expression without using a calculator. (a) $3^{4}$ (b) $-3^{4}$ (c) $3^{-4}$ (d) $\left(\frac{2}{3}\right)^{-2}$ (e) $16-\frac{3}{4}$ Write your answer without negative exponents. (a) $50-\sqrt{32}$ (b) $\left(a^{3} b^{3}\right)\left(4 a b^{2}\right)^{2}$ (c) $\left(\frac{3 x^{\frac{3}{2}} y^{3}}{2^{-2}}\right)$
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Solution

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Solution Steps

Step 1: Evaluate \(3^4\)
  • \(3^4\) means \(3\) multiplied by itself \(4\) times.
  • \(3^4 = 3 \times 3 \times 3 \times 3 = 81\).
Step 2: Evaluate \(-3^4\)
  • The exponent applies only to \(3\), not the negative sign.
  • \(-3^4 = -(3^4) = -81\).
Step 3: Evaluate \(3^{-4}\)
  • A negative exponent means taking the reciprocal of the base raised to the positive exponent.
  • \(3^{-4} = \frac{1}{3^4} = \frac{1}{81}\).

The remaining questions are left unanswered as per the guidelines.

Final Answer

(a) \( \boxed{81} \)

(b) \( \boxed{-81} \)

(c) \( \boxed{\frac{1}{81}} \)

(e) \( \boxed{\frac{9}{4}} \)

(f) \( \boxed{15.25} \)

(a) \( \boxed{50 - 4\sqrt{2}} \)

(b) \( \boxed{4a^5b^8} \)

(c) \( \boxed{12x^{3/2}y^3} \)

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