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 343^4
  • 343^4 means 33 multiplied by itself 44 times.
  • 34=3×3×3×3=813^4 = 3 \times 3 \times 3 \times 3 = 81.
Step 2: Evaluate −34-3^4
  • The exponent applies only to 33, not the negative sign.
  • −34=−(34)=−81-3^4 = -(3^4) = -81.
Step 3: Evaluate 3−43^{-4}
  • A negative exponent means taking the reciprocal of the base raised to the positive exponent.
  • 3−4=134=1813^{-4} = \frac{1}{3^4} = \frac{1}{81}.

The remaining questions are left unanswered as per the guidelines.

Final Answer

(a) 81 \boxed{81}

(b) −81 \boxed{-81}

(c) 181 \boxed{\frac{1}{81}}

(e) 94 \boxed{\frac{9}{4}}

(f) 15.25 \boxed{15.25}

(a) 50−42 \boxed{50 - 4\sqrt{2}}

(b) 4a5b8 \boxed{4a^5b^8}

(c) 12x3/2y3 \boxed{12x^{3/2}y^3}

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