Question

1. Express 4 factors of -20: (-20%)(-2)(-20)(-28)
2. Expand the expression:
-2.-2.-2.-2..0.0.
3. Simplify to the exponential form: (-2)4. (4574
4. Evaluate the base 2 power: 16. (054
5. Apply the power of a power: 162"
What is the value of x in the simplified power? x=

Answer 1

The value of x in the simplified power is 20.

Solution:

Given expression: $\left(-2 d^{5}\right)^{4}$

Step 1: Express 4 factors of $-2 d^{5}$

$\left(-2 d^{5}\right)\left(-2 d^{5}\right)\left(-2 d^{5}\right)\left(-2 d^{5}\right)$

Step 2: Expand the expression

$-2 \cdot-2 \cdot-2 \cdot-2 \cdot d^{5} \cdot d^{5} \cdot d^{5} \cdot d^{5}$

Step 3: Simplify to the exponential form

There four -2 terms and four $d^5$ terms.

$(-2)^{4} \cdot\left(d^{5}\right)^{4}$

Step 4: Evaluate the base 2 power.

$(-2)^{4}=16$

$(-2)^{4} \cdot\left(d^{5}\right)^{4}=16 \cdot\left(d^{5}\right)^{4}$

Step 5: Apply the power of a power.

Using exponent rule: $(a^m)^n=a^{mn}$

So that $\left(d^{5}\right)^{4}=d^{5\times4}=d^{20}$

$16 \cdot\left(d^{5}\right)^{4}=16d^{20}$

$16 d^{x}=16 d^{20}$

⇒ x = 20

The value of x in the simplified power is 20.