Answer :
Sure! Let's go through the process step-by-step to simplify the given expression:
We are given the algebraic expression:
[tex]\[ 9x^4y^3 \cdot 5x^2y^{-5}z^0 \][/tex]
We need to simplify this expression by following these steps:
1. Multiply the Coefficients:
- The coefficients are the numbers in front of the variables. Here, the coefficients are 9 and 5.
- Multiply these coefficients: [tex]\( 9 \times 5 = 45 \)[/tex].
2. Combine the Exponents of [tex]\( x \)[/tex]:
- For [tex]\( x \)[/tex], use the rule [tex]\( x^a \cdot x^b = x^{a+b} \)[/tex].
- The exponents for [tex]\( x \)[/tex] are 4 and 2.
- Add these exponents together: [tex]\( 4 + 2 = 6 \)[/tex].
- So, we have [tex]\( x^6 \)[/tex].
3. Combine the Exponents of [tex]\( y \)[/tex]:
- Similarly, for [tex]\( y \)[/tex], the exponents are 3 and -5.
- Add these exponents together: [tex]\( 3 + (-5) = -2 \)[/tex].
- So, we have [tex]\( y^{-2} \)[/tex].
4. Handle [tex]\( z^0 \)[/tex]:
- Any variable raised to the power of 0 equals 1. So, [tex]\( z^0 = 1 \)[/tex].
- This means it does not affect the product and can be ignored in the simplified expression.
After following all the steps, the simplified expression is:
[tex]\[ 45x^6y^{-2} \][/tex]
This represents the entire process and leads us to the simplified expression provided.
We are given the algebraic expression:
[tex]\[ 9x^4y^3 \cdot 5x^2y^{-5}z^0 \][/tex]
We need to simplify this expression by following these steps:
1. Multiply the Coefficients:
- The coefficients are the numbers in front of the variables. Here, the coefficients are 9 and 5.
- Multiply these coefficients: [tex]\( 9 \times 5 = 45 \)[/tex].
2. Combine the Exponents of [tex]\( x \)[/tex]:
- For [tex]\( x \)[/tex], use the rule [tex]\( x^a \cdot x^b = x^{a+b} \)[/tex].
- The exponents for [tex]\( x \)[/tex] are 4 and 2.
- Add these exponents together: [tex]\( 4 + 2 = 6 \)[/tex].
- So, we have [tex]\( x^6 \)[/tex].
3. Combine the Exponents of [tex]\( y \)[/tex]:
- Similarly, for [tex]\( y \)[/tex], the exponents are 3 and -5.
- Add these exponents together: [tex]\( 3 + (-5) = -2 \)[/tex].
- So, we have [tex]\( y^{-2} \)[/tex].
4. Handle [tex]\( z^0 \)[/tex]:
- Any variable raised to the power of 0 equals 1. So, [tex]\( z^0 = 1 \)[/tex].
- This means it does not affect the product and can be ignored in the simplified expression.
After following all the steps, the simplified expression is:
[tex]\[ 45x^6y^{-2} \][/tex]
This represents the entire process and leads us to the simplified expression provided.
