Question

simplify. \\(\dfrac{4x^{5}z^{5}b^{7}}{x^{6}z}\\)

Explanation:

Step1: Simplify the coefficient

The coefficient is \( 45b^7 \) in the numerator and no coefficient in the denominator (we can consider the denominator's coefficient as 1 for the \( x^6z \) term, but actually, we focus on the variables and the coefficient \( 45 \) and the rest. Wait, maybe the original expression is \( \frac{45b^7xz}{x^6z} \)? Let's assume the expression is \( \frac{45b^7xz}{x^6z} \). First, simplify the \( x \) terms. Using the rule \( \frac{x^m}{x^n}=x^{m - n} \), for \( x \): \( x^1\) in numerator and \( x^6 \) in denominator, so \( x^{1-6}=x^{-5}=\frac{1}{x^5} \).

Step2: Simplify the \( z \) terms

For \( z \): \( z^1 \) in numerator and \( z^1 \) in denominator, so \( z^{1 - 1}=z^0 = 1 \) (they cancel out).

Step3: Simplify the coefficient and \( b \) term

The coefficient is \( 45 \), and the \( b^7 \) term remains as it is. So putting it together: \( 45b^7\times\frac{1}{x^5}\times1=\frac{45b^7}{x^5} \). Wait, maybe the original expression was \( \frac{45b^7xz}{x^6z} \). Let's re - check. If the expression is \( \frac{45b^{7}xz}{x^{6}z} \), then:

• For \( x \): \( x^{1}\div x^{6}=x^{1 - 6}=x^{-5}=\frac{1}{x^{5}} \)
• For \( z \): \( z^{1}\div z^{1}=z^{0}=1 \)
• The coefficient \( 45 \) and \( b^{7} \) stay.

So the simplified form is \( \frac{45b^{7}}{x^{5}} \).

Answer:

\( \frac{45b^{7}}{x^{5}} \)