Question

question 19
use the properties of exponents to simplify the following as much as possible.
$x^5 \cdot x^3 = \square$
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question 20
use the properties of exponents to simplify the following as much as possible.
$(2^2)^5 = \square$
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Explanation:

Step1: Apply product of exponents rule

When multiplying terms with the same base, add exponents: $x^a \cdot x^b = x^{a+b}$.
$x^5 \cdot x^3 = x^{5+3}$

Step2: Calculate the sum of exponents

$x^{5+3} = x^8$

Step3: Apply power of a power rule

When raising a power to a power, multiply exponents: $(a^b)^c = a^{b \cdot c}$.
$(2^2)^5 = 2^{2 \cdot 5}$

Step4: Calculate the product of exponents

$2^{2 \cdot 5} = 2^{10}$

Step5: Compute the final numerical value

$2^{10} = 1024$

Answer:

Question 19: $x^8$
Question 20: $1024$ (or $2^{10}$)