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Exponents

Exponent or Index Notation Exponent Laws Zero and Negative Exponents Rational Exponents Part 1 Rational Exponents Part 2 Standard Form Highest Common Factor and Lowest Common Multiple

Extension Problems

Without listing all the factors, can you find how many factors each number has?
a) 2401
b) 168
c) 1764

a)

b)

c)

Simplify.
$\left(x^\frac{1}{a-b}\right)^\frac{1}{a-c} \left(x^\frac{1}{b-c}\right)^\frac{1}{b-a} \left(x^\frac{1}{c-a}\right)^\frac{1}{c-b}$

If $x^\frac{1}{2}+x^{-\frac{1}{2}}=a$, write $x^2+x^{-2}$ in terms of $a$.

Find the solution that is not $x=0$ or $x=1$ for the following:
$$\left(\sqrt[4]{x}\right)^{4x^4}=\left(x^4\right)^{4\sqrt[4]{x}}$$
Give your answer as an exponent.

$x=$

Solve for $x$.
$4^{\sqrt{x^2-2}+x}-5\cdot2^{x-1+\sqrt{x^2-2}}=6$

$x=$
How many digits does $8^5 \times 5^{10} \times 15^5$ have when evaluated?

Solve for $x$. $$3^x=x^9$$

$x=$