Expressions with exponents and radicals
Expressions with Exponents and Radicals III
Submitted by michaela.bailova on Wed, 10/16/2024 - 13:322000009408
Level:
A
Choose a false statement.
\( 2^4\cdot 4^2 > 2^3\cdot 4^3\)
\(3^8=9^4\)
\( \sqrt{3} + \sqrt{6} > \sqrt{3+6}\)
\(\sqrt{2}\cdot \sqrt{2} = \sqrt{2+2}\)
2000009407
Level:
A
For \(x \in \mathbb{R}\), \(x \neq 0\), simplify the expression \( \frac{x^{-3}x^4}{(x^{-2})^3}\).
\(x^7\)
\(x^2\)
\(1\)
\(x^{-5}\)
2000009406
Level:
A
For \(x\), \(a\), \(b \in \mathbb{R}\), \(x>0\), simplify the expression \( \sqrt{\frac{x^{a-b}}{x^{b-a}}}\).
\(x^{a-b}\)
\(x^{-\frac12}\)
\(1\)
\(-1\)
2000009405
Level:
A
The expression \( \frac{6^3\cdot 50^2}{2^3 \cdot 3^3 \cdot 10^2}\) equals:
\(25\)
\(5\)
\(1.25\)
\(\frac1{125}\)
2000009404
Level:
A
The expression \( \frac{31 \cdot 10^3 \cdot 0.001}{10^4 \cdot 10^{-2}}\) equals:
\(0.31\)
\(3.1\)
\(3100\)
\(310\)
2000009403
Level:
B
The expression \( \sqrt[5]{1024}\) equals:
\(4\)
\(32\)
\(\sqrt{2}\)
\(25\)
2000009402
Level:
A
The expression \( \left(2\left(4\left(6\cdot 8^0\right)^1\right)^{-1}\right)^2\) equals:
\(\frac1{144}\)
\(\frac1{1152}\)
\(6\)
\(0\)
2000009401
Level:
A
The expression \( 5^{12} +5^{11}+5^{10}-6\cdot 5^{10}\) equals:
\(5^{12}\)
\(5^{-27}\)
\(19\cdot 5^{10}\)
\(-15^{23}\)