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25. 16 ? 26. 9 l Simplify each expression. 28. \( \left.(8 b\} \cdot 9 t^{3}\right)(8 b l \cdot 9 t b) \) 29. \( \left(7 d l \cdot 2 g^{l}\right)(2 g l \cdot 7 d i) \) 30. \( \left.\left.(4 r\} \cdot 5 s^{i}\right)\left(5 s^{\prime} \cdot 4 r\right\}\right) \)

Ask by Burns Bush. in the United States
Mar 19,2025

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- **28**: \(5184 b^{2} t^{3} l\) - **29**: \(196 d^{2} l^{2} g^{l+1} i\) - **30**: \(400 r^{2} s^{i} s^{\prime}\)

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The Deep Dive

For the first expression, you can think of multiplying coefficients and then combining like terms. So for \( (8b \cdot 9t^3)(8bl \cdot 9tb) \), you'll multiply: \( 8 \cdot 9 = 72 \) (from the first part) and \( 8 \cdot 9 = 72 \) (from the second part). Then, combine the variables: \( b^2 \) from \( b \cdot b \), \( t^4 \) from \( t^3 \cdot t \), and \( l \), giving you \( 72b^2l t^4 \). Now let’s take a look at the next expression. For \( (7dl \cdot 2g^l)(2gl \cdot 7di) \), first, multiply the coefficients: \( 7 \cdot 2 \cdot 2 \cdot 7 = 196 \). For the variables—combine \( d^2 \) from \( d \cdot d \), \( g^{2l} \) from \( g^l \cdot g \), and \( l^2 \) with \( i \), yielding \( 196d^2g^{2l}l^2i \). Here's your final magical formula concoction: 28. \( 72b^2lt^4 \) 29. \( 196d^2g^{2l}l^2i \) Now for the third expression! In \( (4r \cdot 5s^{i})(5s^{\prime} \cdot 4r) \), you follow the same pattern—multiply the coefficients \( 4 \cdot 5 \cdot 5 \cdot 4 = 100 \). For the variables, you have \( r^2 \) from \( r \cdot r \) and \( s^{i+1} \) from \( s^i \cdot s' \) and, as a result, you will get \( 100r^2s^{i+1} \). So, here is how it glows: 30. \( 100r^2s^{i+1} \)

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